Search results for: Meshless Particle Method

Authors: M. Jalali Azizpour, D. Sajedipour, H. Mohammadi Majd, M.R. Tahmasbi Birgani, M.Rabiae

Abstract:

An explicit axisymmetrical FE methodology is developed here to study the particle temperature arising in WC-Co particle on an AISI 1045 steel substrate. Parameters of constitutive Johnson-cook model were used for simulation. The results show that particle velocity and kinetic energy have important role in temperature arising of particles.

Keywords: FEM, HVOF, Interfacial Temperature, Splat

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Authors: G. Parmar, S. Mukherjee, R. Prasad

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The authors present an algorithm for order reduction of linear time invariant dynamic systems using the combined advantages of the eigen spectrum analysis and the error minimization by particle swarm optimization technique. Pole centroid and system stiffness of both original and reduced order systems remain same in this method to determine the poles, whereas zeros are synthesized by minimizing the integral square error in between the transient responses of original and reduced order models using particle swarm optimization technique, pertaining to a unit step input. It is shown that the algorithm has several advantages, e.g. the reduced order models retain the steady-state value and stability of the original system. The algorithm is illustrated with the help of two numerical examples and the results are compared with the other existing techniques.

Keywords: Eigen spectrum, Integral square error, Orderreduction, Particle swarm optimization, Stability.

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Authors: S. Y. Ahmadi-Brooghani, H. Hassanzadeh, P. Kahhal

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This work presents a study on the abrasive water jet (AWJ) machining. An explicit finite element analysis (FEA) of single abrasive particle impact on stainless steel 1.4304 (AISI 304) is conducted. The abrasive water jet machining is modeled by FEA software ABAQUS/CAE. Shapes of craters in FEM simulation results were used and compared with the previous experimental and FEM works by means of crater sphericity. The influence of impact angle and particle velocity was observed. Adaptive mesh domain is used to model the impact zone. Results are in good agreement with those obtained from the experimental and FEM simulation. The crater-s depth is also obtained for different impact angle and abrasive particle velocities.

Keywords: Abrasive water jet machining, Adaptive meshcontrol, Explicit finite elements analysis, Single-particle impact.

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Authors: Y. Harold Robinson, M. Rajaram, Honey Raju

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Image segmentation and color identification is an important process used in various emerging fields like intelligent robotics. A method is proposed for the manipulator to grasp and place the color object into correct location. The existing methods such as PSO, has problems like accelerating the convergence speed and converging to a local minimum leading to sub optimal performance. To improve the performance, we are using watershed algorithm and for color identification, we are using EPSO. EPSO method is used to reduce the probability of being stuck in the local minimum. The proposed method offers the particles a more powerful global exploration capability. EPSO methods can determine the particles stuck in the local minimum and can also enhance learning speed as the particle movement will be faster.

Keywords: Color information, EPSO, hue, saturation, value (HSV), image segmentation, particle swarm optimization (PSO). Active Contour, GMM.

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Authors: Anurag Gaur, Nidhi, Shashi Sharma

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Targeted drug delivery is a method of delivering medication to a patient in a manner that increases the concentration of the medication in some parts of the body relative to others. Targeted drug delivery seeks to concentrate the medication in the tissues of interest while reducing the relative concentration of the medication in the remaining tissues. This improves efficacy of the while reducing side effects. In the present work, we investigate the effect of magnetic field, flow rate and particle concentration on the capturing of magnetic particles transported in a stent implanted fluidic channel. Iron oxide magnetic nanoparticles (Fe3O4) nanoparticles were synthesized via co-precipitation method. The synthesized Fe3O4 nanoparticles were added in the de-ionized (DI) water to prepare the Fe3O4 magnetic particle suspended fluid. This fluid is transported in a cylindrical tube of diameter 8 mm with help of a peristaltic pump at different flow rate (25-40 ml/min). A ferromagnetic coil of SS 430 has been implanted inside the cylindrical tube to enhance the capturing of magnetic nanoparticles under magnetic field. The capturing of magnetic nanoparticles was observed at different magnetic magnetic field, flow rate and particle concentration. It is observed that capture efficiency increases from 47-67% at magnetic field 2-5kG, respectively at particle concentration 0.6mg/ml and at flow rate 30 ml/min. However, the capture efficiency decreases from 65 to 44% by increasing the flow rate from 25 to 40 ml/min, respectively. Furthermore, it is observed that capture efficiency increases from 51 to 67% by increasing the particle concentration from 0.3 to 0.6 mg/ml, respectively.

Keywords: Capture efficiency, Implant assisted-Magnetic drug targeting (IA-MDT), Magnetic nanoparticles, in vitro study.

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Authors: N. Janjamraj, A. Oonsivilai

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This paper present the harmonic elimination of hybrid multilevel inverters (HMI) which could be increase the number of output voltage level. Total Harmonic Distortion (THD) is one of the most important requirements concerning performance indices. Because of many numbers output levels of HMI, it had numerous unknown variables of eliminate undesired individual harmonic and THD nonlinear equations set. Optimized harmonic stepped waveform (OHSW) is solving switching angles conventional method, but most complicated for solving as added level. The artificial intelligent techniques are deliberation to solve this problem. This paper presents the Particle Swarm Optimization (PSO) technique for solving switching angles to get minimum THD and eliminate undesired individual harmonics of 15-levels hybrid multilevel inverters. Consequently it had many variables and could eliminate numerous harmonics. Both advantages including high level of inverter and Particle Swarm Optimization (PSO) are used as powerful tools for harmonics elimination.

Keywords: Multilevel Inverters, Particle Swarms Optimization, Harmonic Elimination.

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Authors: N. Phanthuna V. Phupha N. Rugthaicharoencheep, S. Lerdwanittip

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This paper presents an optimization technique to economic load dispatch (ELD) problems with considering the daily load patterns and generator constraints using a particle swarm optimization (PSO). The objective is to minimize the fuel cost. The optimization problem is subject to system constraints consisting of power balance and generation output of each units. The application of a constriction factor into PSO is a useful strategy to ensure convergence of the particle swarm algorithm. The proposed method is able to determine, the output power generation for all of the power generation units, so that the total constraint cost function is minimized. The performance of the developed methodology is demonstrated by case studies in test system of fifteen-generation units. The results show that the proposed algorithm scan give the minimum total cost of generation while satisfying all the constraints and benefiting greatly from saving in power loss reduction

Keywords: Particle Swarm Optimization, Economic Load Dispatch, Generator Constraints.

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Authors: Chun-Yao Lee, Yi-Xing Shen, Jung-Cheng Cheng, Yi-Yin Li, Chih-Wen Chang

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This paper proposes the method combining artificial neural network (ANN) with particle swarm optimization (PSO) to implement the maximum power point tracking (MPPT) by controlling the rotor speed of the wind generator. First, the measurements of wind speed, rotor speed of wind power generator and output power of wind power generator are applied to train artificial neural network and to estimate the wind speed. Second, the method mentioned above is applied to estimate and control the optimal rotor speed of the wind turbine so as to output the maximum power. Finally, the result reveals that the control system discussed in this paper extracts the maximum output power of wind generator within the short duration even in the conditions of wind speed and load impedance variation.

Keywords: Maximum power point tracking, artificial neuralnetwork, particle swarm optimization.

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Authors: Sofia Ayouche, Rachid Ellaia, Rajae Aboulaich

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Today, insurers may use the yield curve as an indicator evaluation of the profit or the performance of their portfolios; therefore, they modeled it by one class of model that has the ability to fit and forecast the future term structure of interest rates. This class of model is the Nelson-Siegel-Svensson model. Unfortunately, many authors have reported a lot of difficulties when they want to calibrate the model because the optimization problem is not convex and has multiple local optima. In this context, we implement a hybrid Particle Swarm optimization and Nelder Mead algorithm in order to minimize by least squares method, the difference between the zero-coupon curve and the NSS curve.

Keywords: Optimization, zero-coupon curve, Nelson-Siegel- Svensson, Particle Swarm Optimization, Nelder-Mead Algorithm.

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Authors: Phoevos K. Koukouvinis, John S. Anagnostopoulos, Dimitris E. Papantonis

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This work is an attempt to use the standard Smoothed Particle Hydrodynamics methodology for the simulation of the complex unsteady, free-surface flow in a rotating Turgo impulse water turbine. A comparison of two different geometries was conducted. The SPH method due to its mesh-less nature is capable of capturing the flow features appearing in the turbine, without diffusion at the water/air interface. Furthermore results are compared with a commercial CFD package (Fluent®) and the SPH algorithm proves to be capable of providing similar results, in much less time than the mesh based CFD program. A parametric study was also performed regarding the turbine inlet angle.

Keywords: Smoothed Particle Hydrodynamics, Mesh-lessmethods, Impulse turbines, Turgo turbine.

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Authors: Hosein Falahaty, Hitoshi Gotoh, Abbas Khayyer

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Performance of a Hamiltonian based particle method in simulation of nonlinear structural dynamics is subjected to investigation in terms of stability and accuracy. The governing equation of motion is derived based on Hamilton's principle of least action, while the deformation gradient is obtained according to Weighted Least Square method. The hyper-elasticity models of Saint Venant-Kirchhoff and a compressible version similar to Mooney- Rivlin are engaged for the calculation of second Piola-Kirchhoff stress tensor, respectively. Stability along with accuracy of numerical model is verified by reproducing critical stress fields in static and dynamic responses. As the results, although performance of Hamiltonian based model is evaluated as being acceptable in dealing with intense extensional stress fields, however kinds of instabilities reveal in the case of violent collision which can be most likely attributed to zero energy singular modes.

Keywords: Hamilton's principle of least action, particle based method, hyper-elasticity, analysis of stability.

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Authors: Anurag Sharma, Christian W. Omlin

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Self-organizing map (SOM) is a well known data reduction technique used in data mining. It can reveal structure in data sets through data visualization that is otherwise hard to detect from raw data alone. However, interpretation through visual inspection is prone to errors and can be very tedious. There are several techniques for the automatic detection of clusters of code vectors found by SOM, but they generally do not take into account the distribution of code vectors; this may lead to unsatisfactory clustering and poor definition of cluster boundaries, particularly where the density of data points is low. In this paper, we propose the use of an adaptive heuristic particle swarm optimization (PSO) algorithm for finding cluster boundaries directly from the code vectors obtained from SOM. The application of our method to several standard data sets demonstrates its feasibility. PSO algorithm utilizes a so-called U-matrix of SOM to determine cluster boundaries; the results of this novel automatic method compare very favorably to boundary detection through traditional algorithms namely k-means and hierarchical based approach which are normally used to interpret the output of SOM.

Keywords: cluster boundaries, clustering, code vectors, data mining, particle swarm optimization, self-organizing maps, U-matrix.

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Authors: I. M. Yusuff, O. M. Oni, A. A. Aremu

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Percentage of soil-gas radon-222 concentration (²²²Rn) from soil-depths contributing to outdoor radon atmospheric level depends largely on some physical parameters of the soil. To determine its dependency in soil-depths, survey tests were carried out on soil depths and grain size particles using in-situ measurement method of soil-gas radon-222 concentration at different soil depths. The measurements were carried out with an electronic active radon detector (RAD-7) manufactured by Durridge Company USA. Radon-222 concentrations (²²²Rn) in soil-gas were measured at four different soil depths of 20, 40, 60 and 100 cm in five feasible locations. At each soil depth, soil samples were collected for grain size particle analysis using soil grasp sampler. The result showed that highest value of radon-222 concentration (24,680 ± 1960 Bqm^-3) was measured at 100 cm depth with utmost grain size particle of 17.64% while the lowest concentration (7370 ± 1139 Bqm^-3) was measured at 100 cm depth with least grain size particle of 10.75% respectively. A computational model was derived using SPSS regression package. This model could be a yardstick for prediction on soil gas radon concentration reference to soil grain size particle at different soil-depths.

Keywords: Concentration, radon, porosity, diffusion, colorectal, emanation, yardstick.

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Authors: J. J. Peña, J. Morales, J. García-Ravelo, L. Arcos-Díaz

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The Point canonical transformation method is applied for solving the Schrödinger equation with position-dependent mass. This class of problem has been solved for continuous mass distributions. In this work, a staggered mass distribution for the case of a free particle in an infinite square well potential has been proposed. The continuity conditions as well as normalization for the wave function are also considered. The proposal can be used for dealing with other kind of staggered mass distributions in the Schrödinger equation with different quantum potentials.

Keywords: Free particle, point canonical transformation method, position-dependent mass, staggered mass distribution.

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Authors: İnci M. Erhan

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A numerical method for solving the time-independent Schrödinger equation of a particle moving freely in a three-dimensional axisymmetric region is developed. The boundary of the region is defined by an arbitrary analytic function. The method uses a coordinate transformation and an expansion in eigenfunctions. The effectiveness is checked and confirmed by applying the method to a particular example, which is a prolate spheroid.

Keywords: Bessel functions, Eigenfunction expansion, Quantum billiard, Schrödinger equation, Spherical harmonics

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Authors: Y. Harold Robinson, E. Golden Julie, P. Joyce Beryl Princess

Abstract:

Image segmentation is the concept of splitting the images into several images. Image Segmentation algorithm is used to manipulate the process of image segmentation. The advantage of ABC is that it conducts every worldwide exploration and inhabitant exploration for iteration. Particle Swarm Optimization (PSO) and Evolutionary Particle Swarm Optimization (EPSO) encompass a number of search problems. Cleverness Artificial Bee Colony algorithm has been imposed to increase the performance of a neighborhood search. The simulation results clearly show that the presented ABC methods outperform the existing methods. The result shows that the algorithms can be used to implement the manipulator for grasping of colored objects. The efficiency of the presented method is improved a lot by comparing to other methods.

Keywords: Color information, EPSO, ABC, image segmentation, particle swarm optimization, active contour, GMM.

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Authors: Sijie Fu, Pascal-Henry Biwolé, Christian Mathis

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Among modern airflow measurement methods, Particle Image Velocimetry (PIV) and Particle Tracking Velocimetry (PTV), as visualized and non-instructive measurement techniques, are playing more important role. This paper conducts a comparative experimental study for airflow measurement employing both techniques with the same condition. Velocity vector fields, velocity contour fields, voticity profiles and turbulence profiles are selected as the comparison indexes. The results show that the performance of both PIV and PTV techniques for airflow measurement is satisfied, but some differences between the both techniques are existed, it suggests that selecting the measurement technique should be based on a comprehensive consideration.

Keywords: PIV, PTV, airflow measurement.

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Authors: Houda Abadlia, Nadia Smairi, Khaled Ghedira

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Multiobjective Particle Swarm Optimization (MOPSO) has shown an effective performance for solving test functions and real-world optimization problems. However, this method has a premature convergence problem, which may lead to lack of diversity. In order to improve its performance, this paper presents a hybrid approach which embedded the MOPSO into the island model and integrated a local search technique, Variable Neighborhood Search, to enhance the diversity into the swarm. Experiments on two series of test functions have shown the effectiveness of the proposed approach. A comparison with other evolutionary algorithms shows that the proposed approach presented a good performance in solving multiobjective optimization problems.

Keywords: Particle swarm optimization, migration, variable neighborhood search, multiobjective optimization.

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Authors: Mohammad Izadkhah, Mojtaba Hoseini, Alireza Khalili Tehrani

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In this paper we presented a new method for tracking flying targets in color video sequences based on contour and kernel. The aim of this work is to overcome the problem of losing target in changing light, large displacement, changing speed, and occlusion. The proposed method is made in three steps, estimate the target location by particle filter, segmentation target region using neural network and find the exact contours by greedy snake algorithm. In the proposed method we have used both region and contour information to create target candidate model and this model is dynamically updated during tracking. To avoid the accumulation of errors when updating, target region given to a perceptron neural network to separate the target from background. Then its output used for exact calculation of size and center of the target. Also it is used as the initial contour for the greedy snake algorithm to find the exact target's edge. The proposed algorithm has been tested on a database which contains a lot of challenges such as high speed and agility of aircrafts, background clutter, occlusions, camera movement, and so on. The experimental results show that the use of neural network increases the accuracy of tracking and segmentation.

Keywords: Video tracking, particle filter, greedy snake, neural network.

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Authors: Yingjie Zhang, Ming Li, Ying Zhang, Jing Zhang, Zuolei Hu

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In the actual start-up process of DC motors, the DC drive system often faces a conflict between energy consumption and acceleration performance. To resolve the conflict, this paper proposes a comprehensive performance index that energy consumption index is added on the basis of classical control performance index in the DC motor starting process. Taking the comprehensive performance index as the cost function, particle swarm optimization algorithm is designed to optimize the comprehensive performance. Then it conducts simulations on the optimization of the comprehensive performance of the DC motor on condition that the weight coefficient of the energy consumption index should be properly designed. The simulation results show that as the weight of energy consumption increased, the energy efficiency was significantly improved at the expense of a slight sacrifice of fastness indicators with the comprehensive performance index method. The energy efficiency was increased from 63.18% to 68.48% and the response time reduced from 0.2875s to 0.1736s simultaneously compared with traditional proportion integrals differential controller in energy saving.

Keywords: Comprehensive performance index, energy consumption, acceleration performance, particle swarm optimal control.

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Authors: Pablo Barrera, Jose M. Canas, Vicente Matellan

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This paper addresses the problem of determining the current 3D location of a moving object and robustly tracking it from a sequence of camera images. The approach presented here uses a particle filter and does not perform any explicit triangulation. Only the color of the object to be tracked is required, but not any precisemotion model. The observation model we have developed avoids the color filtering of the entire image. That and the Monte Carlotechniques inside the particle filter provide real time performance.Experiments with two real cameras are presented and lessons learned are commented. The approach scales easily to more than two cameras and new sensor cues.

Keywords: Monte Carlo sampling, multiple view, particle filters, visual tracking.

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Authors: S. Khamsawang, S. Jiriwibhakorn

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This paper proposes an improved approach based on conventional particle swarm optimization (PSO) for solving an economic dispatch(ED) problem with considering the generator constraints. The mutation operators of the differential evolution (DE) are used for improving diversity exploration of PSO, which called particle swarm optimization with mutation operators (PSOM). The mutation operators are activated if velocity values of PSO nearly to zero or violated from the boundaries. Four scenarios of mutation operators are implemented for PSOM. The simulation results of all scenarios of the PSOM outperform over the PSO and other existing approaches which appeared in literatures.

Keywords: Novel particle swarm optimization, Economic dispatch problem, Mutation operator, Prohibited operating zones, Differential Evolution.

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Authors: Chang, Chun-Lang, Liu, Chun-Kai

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This study, for its research subjects, uses patients who had undergone total knee replacement surgery from the database of the National Health Insurance Administration. Through the review of literatures and the interviews with physicians, important factors are selected after careful screening. Then using Cross Entropy Method, Genetic Algorithm Logistic Regression, and Particle Swarm Optimization, the weight of each factor is calculated and obtained. In the meantime, Excel VBA and Case Based Reasoning are combined and adopted to evaluate the system. Results show no significant difference found through Genetic Algorithm Logistic Regression and Particle Swarm Optimization with over 97% accuracy in both methods. Both ROC areas are above 0.87. This study can provide critical reference to medical personnel as clinical assessment to effectively enhance medical care quality and efficiency, prevent unnecessary waste, and provide practical advantages to resource allocation to medical institutes.

Keywords: Total knee replacement, Case Based Reasoning, Cross Entropy Method, Genetic Algorithm Logistic Regression, Particle Swarm Optimization.

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Authors: M. E. Turan, H. Zengin, E. Cevik, Y. Sun, Y. Turen, H. Ahlatci

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In this study, the effects of B₄C and SiC particle reinforcements on wear properties of magnesium matrix metal composites produced by pressure infiltration method were investigated. AZ91 (9%Al-1%Zn) magnesium alloy was used as a matrix. AZ91 magnesium alloy was melted under an argon atmosphere. The melt was infiltrated to the particles with an appropriate pressure. Wear tests, hardness tests were performed respectively. Microstructure characterizations were examined by light optical (LOM) and scanning electron microscope (SEM). The results showed that uniform particle distributions were achieved in both B₄C and SiC reinforced composites. Wear behaviors of magnesium matrix metal composites changed as a function of type of particles. SiC reinforced composite has better wear performance and higher hardness than B₄C reinforced composite.

Keywords: Magnesium matrix composite, pressure infiltration, SEM, wear.

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Authors: Mat Syai'in, Adi Soeprijanto, Takashi Hiyama

Abstract:

An optimal power flow (OPF) based on particle swarm optimization (PSO) was developed with more realistic generator security constraint using the capability curve instead of only Pmin/Pmax and Qmin/Qmax. Neural network (NN) was used in designing digital capability curve and the security check algorithm. The algorithm is very simple and flexible especially for representing non linear generation operation limit near steady state stability limit and under excitation operation area. In effort to avoid local optimal power flow solution, the particle swarm optimization was implemented with enough widespread initial population. The objective function used in the optimization process is electric production cost which is dominated by fuel cost. The proposed method was implemented at Java Bali 500 kV power systems contain of 7 generators and 20 buses. The simulation result shows that the combination of generator power output resulted from the proposed method was more economic compared with the result using conventional constraint but operated at more marginal operating point.

Keywords: Optimal Power Flow, Generator Capability Curve, Particle Swarm Optimization, Neural Network

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Authors: Ming-Tang Tsai, Chih-Wei Yen

Abstract:

In this paper, an Interactive Compromise Approach with Particle Swarm Optimization(ICA-PSO) is presented to solve the Economic Emission Dispatch(EED) problem. The cost function and emission function are modeled as the nonsmooth functions, respectively. The bi-objective including both the minimization of cost and emission is formulated in this paper. ICA-PSO is proposed to solve EED problem for finding a better compromise solution. The solution methodology can offer a global or near-global solution for decision-making requirements. The effectiveness and efficiency of ICA-PSO are demonstrated by a sample test system. Test results can be shown that the proposed method provide a practical and flexible framework for power dispatch.

Keywords: Interactive Compromise Approach, Emission Control, Economic Dispatch, Particle Swarm Optimization.

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Authors: Weiling Li, Wenqi Zhong, Baosheng Jin, Rui Xiao, Yong Lu, Tingting He

Abstract:

Experiments were performed in a three-phase bubble column to study variations of bubble rise velocities. The dynamic gas disengagement (DGD) technique and the fast response pressure transducers were utilized to investigate the bubble rise in the column. The superficial gas velocity of large bubbles and small bubbles, the rise velocities of larger and small bubble fractions were studied considering the effect of particle sizes. The results show that the superficial gas velocity associated with large bubbles linearly increase as superficial gas velocity increasing. Particle size has little effect on the both large and small bubble superficial gas velocities. The rise velocities of larger bubble fractions are larger than that of small bubble fractions, and it had different tendency at low and high superficial gas velocities when changing the particle sizes. The rise velocities of small bubble fractions increased and then had a decrease tendency when the particle size became greater.

Keywords: Bubble rise velocity, gas–liquid–solid, particle size effect, three–phase bubble column.

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Authors: Kasthurirangan Gopalakrishnan, Naga Shashidhar

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The mechanical properties of granular solids are dependent on the flow of stresses from one particle to another through inter-particle contact. Although some experimental methods have been used to study the inter-particle contacts in the past, preliminary work with these techniques indicated that they do not have the necessary resolution to distinguish between those contacts that transmit the load and those that do not, especially for systems with a wide distribution of particle sizes. In this research, computer simulations are used to study the nature and distribution of contacts in a compact with wide particle size distribution, representative of aggregate size distribution used in asphalt pavement construction. The packing fraction, the mean number of contacts and the distribution of contacts were studied for different scenarios. A methodology to distinguish and compute the fraction of load-bearing particles and the fraction of space-filling particles (particles that do not transmit any force) is needed for further investigation.

Keywords: Computer simulation, three-dimensional particlepacking, coordination number, asphalt concrete, aggregates.

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Authors: Kapse Swapnil, K. Shankar

Abstract:

Aiming at optimizing the weight and deflection of cantilever beam subjected to maximum stress and maximum deflection, Multi-objective Particle Swarm Optimization (MOPSO) with Utopia Point based local search is implemented. Utopia point is used to govern the search towards the Pareto Optimal set. The elite candidates obtained during the iterations are stored in an archive according to non-dominated sorting and also the archive is truncated based on least crowding distance. Local search is also performed on elite candidates and the most diverse particle is selected as the global best. This method is implemented on standard test functions and it is observed that the improved algorithm gives better convergence and diversity as compared to NSGA-II in fewer iterations. Implementation on practical structural problem shows that in 5 to 6 iterations, the improved algorithm converges with better diversity as evident by the improvement of cantilever beam on an average of 0.78% and 9.28% in the weight and deflection respectively compared to NSGA-II.

Keywords: Utopia point, multi-objective particle swarm optimization, local search, cantilever beam.

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Authors: S. Panda, S. K. Tomar, R. Prasad, C. Ardil

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Order reduction of linear-time invariant systems employing two methods; one using the advantages of Routh approximation and other by an evolutionary technique is presented in this paper. In Routh approximation method the denominator of the reduced order model is obtained using Routh approximation while the numerator of the reduced order model is determined using the indirect approach of retaining the time moments and/or Markov parameters of original system. By this method the reduced order model guarantees stability if the original high order model is stable. In the second method Particle Swarm Optimization (PSO) is employed to reduce the higher order model. PSO method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Both the methods are illustrated through numerical examples.

Keywords: Model Order Reduction, Markov Parameters, Routh Approximation, Particle Swarm Optimization, Integral Squared Error, Steady State Stability.

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